As someone who has always been fascinated by the soviet Union and Russian history in general, who did Lenin want to take control of the USSR after his passing? I've read some of his Testaments and I know he often and harshly criticized Stalin as well as Trotsky. So if he had the choice, who would have succeeded him?
Something important to note is that Lenin was not in charge of the Soviet Union. He was the most respected man among equals. Yes, his word carried a lot of weight, but he did not wield unlimited authority over the party and the country.
To answer your question, however, there isn't a clear-cut answer to that question. However, the answer is fairly clearly not Stalin.
Stalin is too rude and this defect, although quite tolerable in our midst and dealing amongst us Communists, becomes intolerable in a General Secretary. That is why I suggest that comrades think of a way of removing Stalin and appointing another man in his stead who in all other respects differs from Comrade Stalin in having only one advantage, namely that of being more tolerant, more loyal, more polite and most considerate to the comrades, less capricious etc. This may appear to be a negligible detail. But I think from the standpoint of what I wrote about the relationship between Stalin and Trotsky, it is not a detail, or is it a detail which can assume decisive importance.
V.I. Lenin, Last Testament
Lenin's last active days were spent organising his fight against the Stalin faction at the Congress. He wrote a letter to Trotsky asking him to take up the defense of the Georgian comrades, and to the Georgian leaders warmly committing himself to their cause. It should be noted that such emphatic expressions as "with all my heart" and "with very best comradely greetings" are very rarely met in the letters of Lenin, who preferred a more restrained style of writing. It was a measure of his commitment to the struggle. It should also be pointed out that Lenin's bloc constituted a political faction - what was later known by the Stalinists as an "anti-party bloc". The Stalinists had already organized their faction which controlled the party machine.
Fotieva, Lenin's secretary, took down Lenin's last notes on the Georgian question, evidently preparation for a speech at the Congress:
Vladimir Ilyich's instructions that a hint be given to Stoltz that he [Lenin] was on the side of the injured party. Someone or other of the injured party to be given to understand that he was on their side. Three moments: 1) One should not fight. 2) Concessions should be made. 3) One cannot compare a large state with a small one. Did Stalin know? Why didn't he react? The name 'deviationist' for a deviation towards chauvinism and Menshevism proves the same deviation with the dominant nation chauvinists. Collected printed matter for Vladimir Ilyich.
I also shook hands with a strongly-built man with a sallow face, black moustache, heavy eyebrows, and black hair worn en brosse. I paid little attention to him. He himself said nothing. He did not seem of sufficient importance to include in my gallery of Bolshevik portraits. If he had been announced then to the assembled Party as the successor of Lenin, the delegates would have roared with laughter. The man was the Georgian Djugashvili, known today to the whole world as Stalin, the man of steel.